Research colloquium: Numerical flow analysis and optimization of run-of-river power plants using shallow water equations

As part of the research colloquium for students, doctoral and habiliation candidates, we cordially invite you to Thursday, February 20, 2025, at 10:00 a.m. in room 3516 (Mönchebergstr. 7). We are pleased to announce the lecture by Dr.-Ing. Lars Ostermann with the title

"Numerical flow analysis and optimization of run-of-river power plantswith the help of shallow water equations"

Summary, authors Dr. Lars Ostermann and Christian Seidel

For the hydraulic engineering design of hydropower plants and their fluid mechanical optimization, experimental investigations on the physical partial model or full model in the hydraulic engineering laboratory are used in addition to the design based purely on empirical values. Fluid mechanical investigations with the aid of numerical flow programs based on 2D and 3D methods are also used in some cases. In the case of 2D methods, shallow water equation-based methods are particularly suitable, as a large number of empirical values are available for these methods due to their widespread use in the investigation of fluid mechanical issues in hydraulic engineering, which are often verified by in-situ measurements. The shallow water equation-based methods are used successfully especially for the investigation of flood events and sediment transport.

As part of the construction of a research hydropower plant for the key technology of high-performance water wheels developed at the TU Braunschweig, a flow model based on shallow water equations with consideration of bed and wall friction with the Manning number was developed for the numerical simulation of the hydropower plant, with which both the power plant flow and the influence of the hydropower plant and its operation on the local river section can be investigated. A finite volume method is used for the discretization of the depth-averaged shallow water equations, whereby the flow vector is calculated using the HLL-MUSCL approach and the time integration is carried out using an explicit method. The discretization of the calculation domain as an unstructured triangular mesh is implemented with an iterative, optimized mesh generator for arbitrary domain geometries with local mesh refinement.

In the works [1,2] it is basically shown that shallow water equation-based methods can also be used to optimize the flow mechanics of hydropower plants. The focus in [2] is on the numerical investigation and optimization of the power plant separation pillar, as this significantly determines the formation of the power plant flow in a hydropower plant and thus has a decisive influence on the functionality and efficiency of the plant.

The design of the upstream and downstream bays is also of great importance for the uniform upstream and downstream flow of the power plant. In addition, the shape of the power plant bay in combination with the separating pillar determines to a large extent the inflow from the watercourse, which is decisive for the trash rack system, and the outflow of the power plant flow into the watercourse, which is decisive for bank and bed stability.

In the fluid mechanical investigation of the planned research power plant, the 2D flow model developed in [3] was therefore used to investigate not only the power plant separation pillar but also the influence of the shape of the upstream and downstream bays in order to evaluate their influence on the hydraulic behaviour of the hydropower plant and to optimize the shape of the bay. The main optimization criteria and the procedure for power plant optimization are worked out with the aid of shallow water equation-based methods. The flow phenomena caused by the influence of the shape of the power plant bay are also shown. 4] also investigated and optimized the descent system integrated in the power plant separation pillar, as this has a decisive influence on ecological continuity and the removal of floating debris and sediment. An optimal flow-mechanical shape of the descent system and its correct integration in the headwater and tailwater are just as important for its functionality as the optimal position of the horizontal screen, which forms a unit with the descent system. The influence of turbulence on power plant optimization is described in [5].

[1] Lars Ostermann, Christian Seidel: The shallow water equation and its application to the investigation of hydropower plants. Proceedings in Applied Mathematics and Mechanics (PAMM), 13:279-280, 2013.

[2] Lars Ostermann, Christian Seidel: 2D and 3D numerical flow analysis of power plant separation piers. Proceedings in Applied Mathematics and Mechanics (PAMM), 14: 625-626, 2014.

[3] Lars Ostermann, Christian Seidel: Numerical flow analysis and optimization of power plant bays in run-of-river power plants. Proceedings in Applied Mathematics and Mechanics (PAMM), 16: 573-574, 2016.

[4] Lars Ostermann, Christian Seidel: Investigation of downstream structures of horizontal rakes using shallow water equations. Proceedings in Applied Mathematics and Mechanics (PAMM), 17: 535-536, 2017.

[5] Anas Alfarra, Christian Seidel, Lars Ostermann,: Numerical flow analysis of power plant separation piers using RANS turbulence models. Proceedings in Applied Mathematics and Mechanics (PAMM), 17: 495-496, 2017.